Question

Prove that $\sec A(1-\sin A)(\sec A+\tan A)=1$

Answer 1

$secA(1-sinA)(secA+tanA)=1$

$\Rightarrow \frac{1}{cosA}(1-sinA)(\frac{1}{cosA}+\frac{sinA}{cosA})$

$\Rightarrow \frac{1}{co{s}^{2}A}(1-sinA)(1+sinA)\Rightarrow \frac{1-si{n}^{2}A}{co{s}^{2}A}=\frac{co{s}^{2}A}{co{s}^{2}A}=1$